Average Error: 0.7 → 0.7
Time: 10.3s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{e^{a} + e^{b}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{e^{a} + e^{b}}
double f(double a, double b) {
        double r1922530 = a;
        double r1922531 = exp(r1922530);
        double r1922532 = b;
        double r1922533 = exp(r1922532);
        double r1922534 = r1922531 + r1922533;
        double r1922535 = r1922531 / r1922534;
        return r1922535;
}
↓
double f(double a, double b) {
        double r1922536 = a;
        double r1922537 = exp(r1922536);
        double r1922538 = b;
        double r1922539 = exp(r1922538);
        double r1922540 = r1922537 + r1922539;
        double r1922541 = r1922537 / r1922540;
        return r1922541;
}

Error

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.7
Target0.0
Herbie0.7
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.7

    \[\frac{e^{a}}{e^{a} + e^{b}}\]

  2. Taylor expanded around -inf 0.7

    \[\leadsto \frac{e^{a}}{\color{blue}{e^{b} + e^{a}}}\]

  3. Final simplification0.7

    \[\leadsto \frac{e^{a}}{e^{a} + e^{b}}\]

Reproduce

herbie shell --seed 2019128 
(FPCore (a b)
  :name "Quotient of sum of exps"

  :herbie-target
  (/ 1 (+ 1 (exp (- b a))))

  (/ (exp a) (+ (exp a) (exp b))))